Skip to main content

Full text of "Analytical Mechanics"

See other formats


CHAPTER VII. CENTER OF MASS  AND  MOMENT  OF INERTIA.
CENTER  OF   MASS.
THERE are two useful conceptions, known as center of mass and moment of inertia, which greatly simplify discussions of the motion of rigid bodies. It is, therefore, desirable to become familiar with these conceptions before taking up the motion of rigid bodies.
114. Definition of Center of Mass.  The center of mass of a system of equal particles is their average position; in other words, it is that point whose distance from any fixed plane is the average of the distances of all the particles of the system.
Let xi, 2, 3, . . . xn denote the distances of the particles of a system from the j/^-plane; then, by the above definition, the distance of the center of mass from the same plane is
~^Xl+X2+Xt +   '      '    +Xn
n
n
When the particles have different masses their distances must be weighted, that is, the distance of each particle must be multiplied by the mass of the particle before taking the average. In this case the distance of the center of mass from the 2/s-plane is defined by the following equation:
(mi + m2 +  -   + wn) x = niiXi + m^x^ +     + mnxn,
140